Prove that $\displaystyle A_4$ has a unique subgroup $\displaystyle V$ of order 4.

I know all 12 elements of $\displaystyle A_4$, and I know $\displaystyle V$ contains $\displaystyle { 1, (12)(34), (13)(24), (14)(23)}$, but how do I prove that $\displaystyle V$ is a unique subgroup?